Complex networks of scalar time series using a data compression algorithm

A representation of scalar time series, which has proved to be useful to derive insights about the underlying process generating the data, is to transform the time series into a complex network. This allows data analysis via the rigor of mathematical graph theory, and characterization through application of a range of complex network metrics. For most of these techniques, however, the size of the network (given by the number of nodes) will scale with the size (length) of the time series, enabling only a statistical description of the network properties. This can be problematic if a detailed study of the fine structure of the network evolution is required. To permit a full network analysis of large-scale time series, this work proposes an intermediate step in the transformation process, where we interpret the compact description of large-scale time series data produced by a compression algorithm as a complex network. We demonstrated that properties of compression networks are capable of distinguishing different dynamical behaviours, even in the presence of noisy data, and that one property, in particular, appears to be a useful discriminating statistic in surrogate data hypothesis tests. We demonstrate these ideas on systems with known dynamical behaviour and show that our approach is capable of identifying changes due to a bifurcation parameter of a chaotic system.